Their music tends to vary a lot, much like the similar band "Rawlins Cross," but they seem to take themselves a lot less seriously. There are sad songs such as "How Did We Get from Saying I Love You..." and "My Apology," which seem to fit "Sea" less well than their bouncier tunes. One of those is the hilariously irreverant "Night Pat Murphy Died," about a bunch of guys who honor their dead friend by getting sozzled, and which contains the lyrics "... we went up to the graveyard/so holy and sublime/found out when we got there/we'd left the corpse behind!" They do a cover of REM's "End of the World" which was so good that I originally thought it was their own song; also there are the delightfully danceable "Rigadoon," "Ordinary Day," or "Jolly Roving Tar." A few aren't as danceable, but still very catchy, like the mostly musicless "General Taylor" or the rhythmic "Donkey Riding."
This Celtic-rock band is probably one of the best out there; you can almost imagine these guys dancing and singing as you listen. Check out this and other albums by Great Big Sea, and don't feel ashamed to sing along. I do it whenever I listen.